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Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?

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#### Solution

A is the position of the 1^{st} train.

B is the position of the 2^{nd} train.

Distance Covered in 2 hours

OA = 2 × 20 = 40 km

OB = 2 × 30 = 60 km

Distance between the train after 2 hours

AB = `sqrt("OA"^2 + "OB"^2)`

= `sqrt(40^2 + 60^2)`

= `sqrt(1600 + 3600)`

= `sqrt(5200)` or `sqrt(52 xx 100)`

= `10sqrt(4 xx 13)`

= `20sqrt(13)`

= 72.11 km

Distance between the two train = 72.11 km or `20sqrt(13) "km"`

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